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Generalized exterior sphere conditions and $\varphi$-convexity

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  • We consider sets $S\subset\R^n$ satisfying a certain exterior sphere condition, and it is shown that under wedgedness of $S$, it coincides with $\varphi$-convexity. We also offer related improvements concerning the union of uniform closed balls conjecture.
    Mathematics Subject Classification: Primary: 49J52; Secondary: 52A20.


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